Eur. Phys. J. Special Topics 222, 615-624 (2013)
https://doi.org/10.1140/epjst/e2013-01867-2

Regular Article

Singular Lagrangian, Hamiltonization and Jacobi last multiplier for certain biological systems

¹ S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata 700098, India
² Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta 700009, India

^a e-mail: partha@bose.res.in
^b e-mail: aghosechoudhury@gmail.com

Received: 22 March 2013
Revised: 3 May 2013
Published online: 11 July 2013

Abstract

We study the construction of singular Lagrangians using Jacobi's last multiplier (JLM). We also demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonian of the Host-Parasite model and a Lotka-Volterra mutualistic system, both of which are well known first-order systems of differential equations arising in biology.